Statistical Models in Biology

STATS215 · Winter 2020 · Stanford University

Course Description

This course is about probabilistic models in biology and the statistical inference algorithms necessary to fit them to data. We will cover some of the most important tools for modeling biological data, including latent variable models, hidden Markov models, dynamical systems, Poisson processes, and recent extensions like variational autoencoders and recurrent neural networks. We will study algorithms for parameter estimation and inference, and we will apply these tools to a variety of problems across biology, with a particular emphasis on applications in neuroscience. In your homework assignments and final project, you will implement these models and algorithms and apply them to real data.

Prerequisites

You should be comfortable with the basics of probability at the level of STAT116, including random variables, joint densities, conditional distributions, etc. You should also be familiar with linear regression and maximum likelihood estimation, for example from STAT200. We will use basic linear algebra (solving linear systems and using eigendecompositions) and multivariable calculus (gradients, Jacobians, Hessians, etc.).

Logistics

• Instructor: Scott Linderman
• Teaching Assistant: Kevin Han
• Lectures: Tuesday and Thursday, 12-1:20pm
• Location: 540-108
• Office Hours:
  • Scott: Tuesday 2-3pm Sequoia Hall Rm 232
  • Kevin: Monday 3-5pm Sequoia Hall Library

Grading

• 4 Assignments: 15% each
• Midterm Exam: 10%
• Final Project Proposal: 5%
• Final Project Report: 20%
• In-class Participation: 5%

Late policy: All assignments are due at 11:59pm PT on the due date. You can turn in homework assignments up to a week late with a 50% penalty on your grade. Final project reports will not be accepted after the deadline.

Midterm: The midterm will be given in class.

Assignments

Assignments consist of math problems and coding problems. You will find a LaTeX template for your write-up in the GitHub folder. Submit a pdf of your write-up and an .ipynb and .pdf of the Google Colab notebook with your completed coding assignment. All submissions should be made through Canvas.

• Assignment 1
• Assignment 2
• Assignment 3
• Assignment 4

Final project

The final project is an opportunity to apply these models and algorithms to datasets of interest to you. Ideally, your project will involve some theory – extending a model to fit the needs of your particular problem and studying its properties – and some experimentation – fitting the model to biological data.

Proposal: Start thinking about what datasets you'd like to study and what questions you'd like to answer early! These will inform your choices about modeling tools. As a forcing function, part of your grade will be based on your proposal, which is due roughly a month before the final report. By this point, you should have a pretty clear idea about the dataset and question, and some initial thoughts about the types of models you will explore and experiments you will run.

Report: The final report will present your theoretical work and experimental results. It should look like the start of a research paper. To that end, you will write it in the NeurIPS paper format, and you will submit a link to a GitHub repository with supporting code.

Readings

The readings are meant to supplement lecture with further details and show examples of how different models are being used in biology. I've listed multiple technical readings and applications – you do not have to read all of them. You may find it helpful to see the same concepts presented in different ways, or you may find that you like some author's style better than others. Likewise, I've listed multiple references for many biological applications; I will reference some of these in class, and if you're curious you can dig into the others as well.

Anticipated Schedule

Textbooks

Barber, D. (2012). Bayesian reasoning and machine learning. Cambridge University Press.

Bishop, C. M. (2006). Pattern recognition and machine learning. Springer.

Ewens, W. J., & Grant, G. (2005). Statistical Methods in Bioinformatics. Springer.
Available in library

Goodfellow, I., Bengio, Y., & Courville, A. (2016). The deep learning book. MIT Press.

Hastie, T., Tibshirani, R., & Friedman, J. (2009). The elements of statistical learning: data mining, inference, and prediction. Springer-Verlag.

Kingman, J. F. C. (1993). Poisson processes. Clarendon Press.
Available in library

MacKay, D. J. (2003). Information theory, inference and learning algorithms. Cambridge university press.

Murphy, K. P. (2012). Machine learning: a probabilistic perspective. MIT press.
Available in library

Williams, C. K., & Rasmussen, C. E. (2006). Gaussian processes for machine learning. MIT press.

Robert, C., & Casella, G. (2013). Monte Carlo statistical methods. Springer.

Wainwright, M. J., & Jordan, M. I. (2008). Graphical models, exponential families, and variational inference. Foundations and Trends® in Machine Learning, 1(1–2), 1-305.